Derivation of linear estimation algorithms from measurements affected by multiplicative and additive noises

Authors:
M. J. García-Ligero;A. Hermoso-Carazo;J. Linares-Pérez;S. Nakamori
Affiliations:
Departamento de Estadística e I.O., Universidad de Granada, Campus Fuentenueva, s/n, 18071 Granada, Spain;Departamento de Estadística e I.O., Universidad de Granada, Campus Fuentenueva, s/n, 18071 Granada, Spain;Departamento de Estadística e I.O., Universidad de Granada, Campus Fuentenueva, s/n, 18071 Granada, Spain;Department of Technology, Faculty of Education, Kagoshima University, Kohrimoto, Kagoshima 890-0065, Japan
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

This paper addresses the problem of estimating signals from observation models with multiplicative and additive noises. Assuming that the state-space model is unknown, the multiplicative noise is non-white and the signal and additive noise are correlated, recursive algorithms are derived for the least-squares linear filter and fixed-point smoother. The proposed algorithms are obtained using an innovation approach and taking into account the information provided by the covariance functions of the process involved.